Physics Q47 – JEE-MAIN 2026

Home Physics Mechanical Properties of FluidsQuestion #258

The surface tension of a soap solution is

3.5 \times 10^{- 2}

N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is

α \times 10^{- 6}

J. The value of

α

is _______ (

π = 22 / 7

)

Enter Calculated Numerical Value:

Clue 1 of 3: Surface Energy

Work done in increasing the size of a soap bubble is equal to the increase in its surface energy.

🧠 Full Solution Path

Step 1: Identify the formula for work done on a soap bubble✦ Active

A soap bubble has two free surfaces (inner and outer). The work done ( $W$ ) to increase its surface area is given by the product of surface tension ( $T$ ) and the total change in surface area ( $Δ A_{t o t a l}$ ). The surface area of a sphere is $4 π r^{2}$ , so for a soap bubble, the total surface area is $2 \times 4 π r^{2} = 8 π r^{2}$ .

W = T \times Δ A_{t o t a l}

Step 2: Calculate the change in total surface area○ Expand

Given initial radius $r_{1} = 1$ cm $= 0.01$ m and final radius $r_{2} = 2$ cm $= 0.02$ m. The change in total surface area is:

Δ A_{t o t a l} = 8 π (r_{2}^{2} - r_{1}^{2})

Δ A_{t o t a l} = 8 \times \frac{22}{7} \times ((0.02)^{2} - (0.01)^{2})

Δ A_{t o t a l} = 8 \times \frac{22}{7} \times (0.0004 - 0.0001)

Δ A_{t o t a l} = 8 \times \frac{22}{7} \times 0.0003

Δ A_{t o t a l} = 8 \times \frac{22}{7} \times 3 \times 10^{- 4} m^{2}

💡 Teacher's Secret Hint

Ensure all units are consistent (SI units) before calculation.

Step 3: Calculate the work done and determine \alpha○ Expand

Given surface tension $T = 3.5 \times 10^{- 2}$ N/m. Now, substitute the values into the work done formula:

W = T \times Δ A_{t o t a l}

W = (3.5 \times 10^{- 2}) \times (8 \times \frac{22}{7} \times 3 \times 10^{- 4})

W = (\frac{7}{2} \times 10^{- 2}) \times (8 \times \frac{22}{7} \times 3 \times 10^{- 4})

W = (4 \times 22 \times 3) \times 10^{- 2} \times 10^{- 4}

W = 264 \times 10^{- 6} J

The problem states that the work required is $α \times 10^{- 6}$ J. Comparing this with our calculated value:

α \times 10^{- 6} = 264 \times 10^{- 6}

α = 264

💡 Teacher's Secret Hint

Pay attention to the powers of 10 and the value of $π$ provided.

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Physics Question 47 – JEE-MAIN 2026

Clue 1 of 3: Surface Energy

🧠 Full Solution Path